arXiv:2603.29361v1 Announce Type: new Abstract: Tree ensembles (TEs) find a multitude of practical applications. They represent one of the most general and accurate classes of machine learning methods. While they are typically quite concise in representation, their operation remains inscrutable to human decision makers. One solution to build trust in the operation of TEs is to automatically identify explanations for the predictions made. Evidently, we can only achieve trust using explanations, if those explanations are rigorous, that is truly reflect properties of the underlying predictor they explain This paper investigates the computation of rigorously-defined, logically-sound explanations for the concrete case of two well-known examples of tree ensembles, namely random forests and boosted trees.

arXiv:2603.29868v1 Announce Type: new Abstract: The reliability of autonomous systems depends on their robustness, i.e., their ability to meet their objectives under uncertainty. In this paper, we study spatiotemporal robustness of temporal logic specifications evaluated over discrete-time signals. Existing work has proposed robust semantics that capture not only Boolean satisfiability, but also the geometric distance from unsatisfiability, corresponding to admissible spatial perturbations of a given signal. In contrast, we propose spatiotemporal robustness (STR), which captures admissible spatial and temporal perturbations jointly. This notion is particularly informative for interacting systems, such as multi-agent robotics, smart cities, and air traffic control. We define STR as a multi-objective reasoning problem, formalized via a partial order over spatial and temporal perturbations. This perspective has two key advantages: (1) STR can be interpreted as a Pareto-optimal set that characterizes all admissible spatiotemporal perturbations, and (2) STR can be computed using tools from multi-objective optimization. To navigate computational challenges, we propose robust semantics for STR that are sound in the sense of suitably under-approximating STR while being computationally tractable. Finally, we present monitoring algorithms for STR using these robust semantics. To the best of our knowledge, this is the first work to deal with robustness across multiple dimensions via multi-objective reasoning.

arXiv:2603.28796v1 Announce Type: cross Abstract: Boolean satisfiability (SAT) problem, the first problem proven to be NP-complete, has become a fundamental challenge in computational complexity, with widespread applications in optimization and verification across many domains. Despite significant algorithmic advances over the past two decades, the performance of SAT solvers has improved at a limited pace. Notably, the 2025 competition winner shows only about a 2X improvement over the 2006 winner in SAT Competition performance after nearly 20 years of effort. This paper introduces GaloisSAT, a novel hybrid GPU-CPU SAT solver that integrates a differentiable SAT solving engine powered by modern machine learning infrastructure on GPUs, followed by a traditional CDCL-based SAT solving stage on CPUs. GaloisSAT is benchmarked against the latest versions of state-of-the-art solvers, Kissat and CaDiCaL, using the SAT Competition 2024 benchmark suite. Results demonstrate substantial improvements in the official SAT Competition metric PAR-2 (penalized average runtime with a timeout of 5,000 seconds and a penalty factor of 2). Specifically, GaloisSAT achieves an 8.41X speedup in the satisfiable category and a 1.29X speedup in the unsatisfiable category compared to the strongest baselines.

arXiv:2508.00017v4 Announce Type: replace-cross Abstract: We present Generative Logic (GL), a deterministic architecture that starts from user-supplied axiomatic definitions written in a minimalist Mathematical Programming Language (MPL) and systematically explores a configurable region of their deductive neighborhood. Definitions are compiled into a distributed grid of Logic Blocks (LBs) that communicate via a unified hash-based inference engine; whenever the premises of a rule unify, a new fact is emitted with full provenance, yielding replayable, auditable proof graphs. The pipeline includes an Incubator that auto-generates ground-level fact tables, a Compressor that eliminates post-proof redundancy, and an independent external Verifier (34,320 checks, zero failures). Experimental validation on Elementary Number Theory develops Peano arithmetic from axioms and autonomously derives Gauss's summation formula. On commodity hardware, the core proving pipeline completes in under one minute; the full run including Incubator fact generation finishes in approximately ten minutes. The Incubator output further reveals that GL can perform concrete numerical calculations -- each result a proved theorem with full provenance -- opening a path toward a full-provenance Computer Algebra System (CAS). Generated proofs export as navigable HTML for independent inspection. Code, proof graphs, and reproduction instructions are available at github.com/Generative-Logic/GL (commit 6e5b9a4) and archived at doi:10.5281/zenodo.17206386.

arXiv:2411.03231v3 Announce Type: replace-cross Abstract: This paper introduces LOGSAFE, a defense mechanism for federated learning in time series settings, particularly within cyber-physical systems. It addresses poisoning attacks by moving beyond traditional update-similarity methods and instead using logical reasoning to evaluate client reliability. LOGSAFE extracts client-specific temporal properties, infers global patterns, and verifies clients against them to detect and exclude malicious participants. Experiments show that it significantly outperforms existing methods, achieving up to 93.27% error reduction over the next best baseline. Our code is available at https://github.com/judydnguyen/LOGSAFE-Robust-FTS.

arXiv:2603.12926v1 Announce Type: new Abstract: The ODRL language has become the standard for representing policies and regulations for digital rights. However its complexity is a barrier to its usage, which has caused many related theoretical and practical works to focus on different, and not interoperable, fragments of ODRL. Moreover, semantically equivalent policies can be expressed in numerous different ways, which makes comparing them and processing them harder. Building on top of a recently defined semantics, we tackle these problems by proposing an approach that involves a parametrised normalisation of ODRL policies into its minimal components which reformulates policies with permissions and prohibitions into policies with permissions exclusively, and simplifies complex logic constraints into simple ones. We provide algorithms to compute a normal form for ODRL policies and simplifying numerical and symbolic constraints. We prove that these algorithms preserve the semantics of policies, and analyse the size complexity of the result, which is exponential on the number of attributes and linear on the number of unique values for these attributes. We show how this makes complex policies representable in more basic fragments of ODRL, and how it reduces the problem of policy comparison to the simpler problem of checking if two rules are identical.

arXiv:2603.12744v1 Announce Type: cross Abstract: Automated theorem proving (ATP) benchmarks largely consist of problems formalized in MathLib, so current ATP training and evaluation are heavily biased toward MathLib's definitional framework. However, frontier mathematics is often exploratory and prototype-heavy, relying on bespoke constructions that deviate from standard libraries. In this work, we evaluate the robustness of current ATP systems when applied to a novel definitional framework, specifically examining the performance gap between standard library problems and bespoke mathematical constructions. We introduce TaoBench, an undergraduate-level benchmark derived from Terence Tao's Analysis I, which formalizes analysis by constructing core mathematical concepts from scratch, without relying on standard Mathlib definitions, as well as by mixing from-scratch and MathLib constructions. For fair evaluation, we build an agentic pipeline that automatically extracts a compilable, self-contained local environment for each problem. To isolate the effect of definitional frameworks, we additionally translate every problem into a mathematically equivalent Mathlib formulation, yielding paired TaoBench-Mathlib statements for direct comparison. While state-of-the-art ATP models perform capably within the MathLib framework, performance drops by an average of roughly 26% on the definitionally equivalent Tao formulation. This indicates that the main bottleneck is limited generalization across definitional frameworks rather than task difficulty. TaoBench thus highlights a gap between benchmark performance and applicability, and provides a concrete foundation for developing and testing provers better aligned with research mathematics.

arXiv:2603.12953v1 Announce Type: cross Abstract: Neuro-symbolic reasoning increasingly demands frameworks that unite the formal rigor of logic with the interpretability of large language models (LLMs). We introduce an end to end explainability by construction pipeline integrating the Automated Theorem Generator Delta1 based on the full triangular standard contradiction (FTSC) with LLMs. Delta1 deterministically constructs minimal unsatisfiable clause sets and complete theorems in polynomial time, ensuring both soundness and minimality by construction. The LLM layer verbalizes each theorem and proof trace into coherent natural language explanations and actionable insights. Empirical studies across health care, compliance, and regulatory domains show that Delta1 and LLM enables interpretable, auditable, and domain aligned reasoning. This work advances the convergence of logic, language, and learning, positioning constructive theorem generation as a principled foundation for neuro-symbolic explainable AI.

arXiv:2603.06710v1 Announce Type: cross Abstract: Mining specifications from execution traces presents an automated way of capturing characteristic system behaviors. However, existing approaches are largely restricted to Boolean abstractions of events, limiting their ability to express data-aware properties. In this paper, we extend mining procedures to operate over richer datatypes. We first establish candidate functions in our domain that cover the set of traces by leveraging Syntax Guided Synthesis (SyGuS) techniques. To capture these function applications temporally, we formalize the semantics of TSL$_f$, a finite-prefix interpretation of Temporal Stream Logic (TSL) that extends LTL$_f$ with support for first-order predicates and functional updates. This allows us to unify a corresponding procedure for learning the data transformations and temporal specifications of a system. We demonstrate our approach synthesizing reactive programs from mined specifications on the OpenAI-Gymnasium ToyText environments, finding that our method is more robust and orders of magnitude more sample-efficient than passive learning baselines on generalized problem instances.

arXiv:2603.06737v1 Announce Type: cross Abstract: We describe an experiment in large-scale autoformalization of algebraic topology in an Interactive Theorem Proving (ITP) environment, where the workload is distributed among multiple LLM-based coding agents. Rather than relying on static central planning, we implement a simulated bounty-based marketplace in which agents dynamically propose new lemmas (formal statements), attach bounties to them, and compete to discharge these proof obligations and claim the bounties. The agents interact directly with the interactive proof system: they can invoke tactics, inspect proof states and goals, analyze tactic successes and failures, and iteratively refine their proof scripts. In addition to constructing proofs, agents may introduce new formal definitions and intermediate lemmas to structure the development. All accepted proofs are ultimately checked and verified by the underlying proof assistant. This setting explores collaborative, decentralized proof search and theory building, and the use of market-inspired mechanisms to scale autoformalization in ITP.

arXiv:2603.06849v1 Announce Type: cross Abstract: Several successful strategies in automated reasoning rely on human-supplied guidance about which term or clause shapes are interesting. In this paper we aim to discover interesting term shapes automatically. Specifically, we discover abstractions : term patterns that occur over and over again in relevant proofs. We present our tool Twitch which discovers abstractions with the help of Stitch, a tool originally developed for discovering reusable library functions in program synthesis tasks. Twitch can produce abstractions in two ways: (1) from a partial, failed proof of a conjecture; (2) from successful proofs of other theorems in the same domain. We have also extended Twee, an equational theorem prover, to use these abstractions. We evaluate Twitch on a set of unit equality (UEQ) problems from TPTP, and show that it can prove 12 rating-1 problems as well as yielding significant speed-ups on many other problems.

arXiv:2603.06974v1 Announce Type: cross Abstract: We present Elenchus, a dialogue system for knowledge base construction grounded in inferentialist semantics, where knowledge engineering is re-conceived as explicitation rather than extraction from expert testimony or textual content. A human expert develops a bilateral position (commitments and denials) about a topic through prover-skeptic dialogue with a large language model (LLM) opponent. The LLM proposes tensions (claims that parts of the position are jointly incoherent) which the expert resolves by retraction, refinement, or contestation. The LLM thus serves as a defeasible derivability oracle whose unreliability is structurally contained by the expert's authority. Our main technical contribution is a mapping from Elenchus dialectical states to material bases in Hlobil and Brandom's NonMonotonic MultiSuccedent (NMMS) logic, satisfying Containment and enabling the elaboration of logical vocabulary that makes explicit the inferential relationships negotiated in the dialectic. We demonstrate the approach on the W3C PROV-O provenance ontology, where a single dialogue session elicits and structures design tensions that a domain expert can articulate, corresponding to decisions documented in a retrospective analysis of the ontology's design. Using pyNMMS, an automated NMMS reasoner, we verify that the structural properties of the resulting material base (nontransitivity, nonmonotonicity, and independence) correspond to specific PROV design rationales, demonstrating end-to-end integration from dialogue through formal reasoning.

arXiv:2506.09487v3 Announce Type: replace-cross Abstract: This paper presents BemaGANv2, an advanced GAN-based vocoder designed for high-fidelity and long-term audio generation, with a focus on systematic evaluation of discriminator combination strategies. Long-term audio generation is critical for applications in Text-to-Music (TTM) and Text-to-Audio (TTA) systems, where maintaining temporal co- herence, prosodic consistency, and harmonic structure over extended durations remains a significant challenge. Built upon the original BemaGAN architecture, BemaGANv2 incorporates major architectural innovations by replacing traditional ResBlocks in the generator with the Anti-aliased Multi-Periodicity composition (AMP) module, which internally applies the Snake activation function to better model periodic structures. In the discriminator framework, we integrate the Multi-Envelope Discriminator (MED), a novel architecture we proposed, to extract rich temporal en- velope features crucial for periodicity detection. Coupled with the Multi-Resolution Discriminator (MRD), this com- bination enables more accurate modeling of long-range dependencies in audio. We systematically evaluate various discriminator configurations, including Multi-Scale Discriminator (MSD) + MED, MSD + MRD, and Multi-Period Discriminator (MPD) + MED + MRD, using objective metrics (Fr\'echet Audio Distance (FAD), Structural Similar- ity Index (SSIM), Pearson Correlation Coefficient (PCC), Mel-Cepstral Distortion (MCD), Multi-Resolution STFT (M-STFT), Periodicity error (Periodicity)) and subjective evaluations (MOS, SMOS). To support reproducibility, we provide detailed architectural descriptions, training configurations, and complete implementation details. The code, pre-trained models, and audio demo samples are available at: https://github.com/dinhoitt/BemaGANv2.

arXiv:2511.02872v4 Announce Type: replace-cross Abstract: Recent advances in large language models (LLMs) have demonstrated impressive capabilities in formal theorem proving, particularly on contest-based mathematical benchmarks like the IMO. However, these contests do not reflect the depth, breadth, and abstraction of modern mathematical research. To bridge this gap, we introduce FATE (Formal Algebra Theorem Evaluation), a new benchmark series in formal algebra designed to chart a course toward advanced mathematical reasoning. We present two new components, FATE-H and FATE-X, each with 100 problems in abstract and commutative algebra. The FATE series spans a difficulty spectrum from undergraduate exercises to problems exceeding PhD qualifying exams. Notably, FATE-X is the first formal benchmark to surpass both PhD-level exam difficulty and the coverage of the Mathlib library. Our evaluations of state-of-the-art LLM provers on this new benchmark reveal a stark performance gap compared to contest math: the best model achieves only 3% (pass@64) accuracy on FATE-H and 0% on FATE-X. Our two-stage evaluation reveals that models' natural-language reasoning is notably more accurate than their ability to formalize this reasoning. We systematically classify the common errors that arise during this formalization process. Furthermore, a comparative study shows that a specialized prover can exhibit less effective reflection than general-purpose models, reducing its accuracy at the natural-language stage. We believe FATE provides a robust and challenging benchmark that establishes essential checkpoints on the path toward research-level formal mathematical reasoning.

arXiv:2603.03971v1 Announce Type: cross Abstract: Generative AI can convert uncertainty into authoritative-seeming verdicts, displacing the justificatory work on which democratic epistemic agency depends. As a corrective, I propose a Brouwer-inspired assertibility constraint for responsible AI: in high-stakes domains, systems may assert or deny claims only if they can provide a publicly inspectable and contestable certificate of entitlement; otherwise they must return "Undetermined". This constraint yields a three-status interface semantics (Asserted, Denied, Undetermined) that cleanly separates internal entitlement from public standing while connecting them via the certificate as a boundary object. It also produces a time-indexed entitlement profile that is stable under numerical refinement yet revisable as the public record changes. I operationalize the constraint through decision-layer gating of threshold and argmax outputs, using internal witnesses (e.g., sound bounds or separation margins) and an output contract with reason-coded abstentions. A design lemma shows that any total, certificate-sound binary interface already decides the deployed predicate on its declared scope, so "Undetermined" is not a tunable reject option but a mandatory status whenever no forcing witness is available. By making outputs answerable to challengeable warrants rather than confidence alone, the paper aims to preserve epistemic agency where automated speech enters public justification.

arXiv:2603.04334v1 Announce Type: cross Abstract: We present SpotIt+, an open-source tool for evaluating Text-to-SQL systems via bounded equivalence verification. Given a generated SQL query and the ground truth, SpotIt+ actively searches for database instances that differentiate the two queries. To ensure that the generated counterexamples reflect practically relevant discrepancies, we introduce a constraint-mining pipeline that combines rule-based specification mining over example databases with LLM-based validation. Experimental results on the BIRD dataset show that the mined constraints enable SpotIt+ to generate more realistic differentiating databases, while preserving its ability to efficiently uncover numerous discrepancies between generated and gold SQL queries that are missed by standard test-based evaluation.

arXiv:2506.08321v2 Announce Type: replace Abstract: This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for provable-correctness, but these are hard for students to learn. We present a proof-of-concept system (LeanTutor) by combining the complementary strengths of LLMs and theorem provers. LeanTutor is composed of three modules: (i) an autoformalizer/proof-checker, (ii) a next-step generator, and (iii) a natural language feedback generator. To evaluate the system, we introduce PeanoBench, a dataset of 371 Peano Arithmetic proofs in human-written natural language and formal language, derived from the Natural Numbers Game.

arXiv:2510.09782v2 Announce Type: replace Abstract: We study how large language models (LLMs) ``think'' through their representation space. We propose a novel geometric framework that models an LLM's reasoning as flows -- embedding trajectories evolving where logic goes. We disentangle logical structure from semantics by employing the same natural deduction propositions with varied semantic carriers, allowing us to test whether LLMs internalize logic beyond surface form. This perspective connects reasoning with geometric quantities such as position, velocity, and curvature, enabling formal analysis in representation and concept spaces. Our theory establishes: (1) LLM reasoning corresponds to smooth flows in representation space, and (2) logical statements act as local controllers of these flows' velocities. Using learned representation proxies, we design controlled experiments to visualize and quantify reasoning flows, providing empirical validation of our theoretical framework. Our findings indicate that training solely via next-token prediction can lead LLMs to internalize logical invariants as higher-order geometry in representation space, challenging the ``stochastic parrot'' argument. Experiments across Qwen and LLaMA model families further suggest the presence of a general, possibly universal, representational law underlying machine understanding and human linguistic regularities, largely independent of specific training recipes or model architectures. Our work serves as both a conceptual foundation and practical tools for studying reasoning phenomena, offering a new lens for interpretability and formal analysis of LLMs' behavior.

arXiv:2510.26840v2 Announce Type: replace-cross Abstract: Community-driven Text-to-SQL evaluation platforms play a pivotal role in tracking the state of the art of Text-to-SQL performance. The reliability of the evaluation process is critical for driving progress in the field. Current evaluation methods are largely test-based, which involves comparing the execution results of a generated SQL query and a human-labeled ground-truth on a static test database. Such an evaluation is optimistic, as two queries can coincidentally produce the same output on the test database while actually being different. In this work, we propose a new alternative evaluation pipeline, called SpotIt, where a formal bounded equivalence verification engine actively searches for a database that differentiates the generated and ground-truth SQL queries. We develop techniques to extend existing verifiers to support a richer SQL subset relevant to Text-to-SQL. A performance evaluation of ten Text-to-SQL methods on the high-profile BIRD dataset suggests that test-based methods can often overlook differences between the generated query and the ground-truth. Further analysis of the verification results reveals a more complex picture of the current Text-to-SQL evaluation.

arXiv:2602.19160v1 Announce Type: new Abstract: This paper examines the reasoning capabilities of Large Language Models (LLMs) from a novel perspective, focusing on their ability to operate within formally specified, rule-governed environments. We evaluate four LLMs (Gemini 2.5 Pro and Flash variants, Llama 3.3 70B and GPT-OSS 120B) on a suite of forward-simulation tasks-including next / multistep state formulation, and legal action generation-across a diverse set of reasoning problems illustrated through General Game Playing (GGP) game instances. Beyond reporting instance-level performance, we characterize games based on 40 structural features and analyze correlations between these features and LLM performance. Furthermore, we investigate the effects of various game obfuscations to assess the role of linguistic semantics in game definitions and the impact of potential prior exposure of LLMs to specific games during training. The main results indicate that three of the evaluated models generally perform well across most experimental settings, with performance degradation observed as the evaluation horizon increases (i.e., with a higher number of game steps). Detailed case-based analysis of the LLM performance provides novel insights into common reasoning errors in the considered logic-based problem formulation, including hallucinated rules, redundant state facts, or syntactic errors. Overall, the paper reports clear progress in formal reasoning capabilities of contemporary models.